Tag: rounding off decimals

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Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

If $x$ and $y$ are positive real number, then which of the following is correct?

  1. $x > y \Rightarrow -x > -y $
  2. $x > y \Rightarrow -x < -y $
  3. $x > y \Rightarrow \dfrac{1}{x} > \dfrac{1}{y} $
  4. $x > y \Rightarrow \dfrac{1}{x} < \dfrac{-1}{y} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If $x$ and $y$ are positive number and $x>y$, then 

$\Rightarrow -x<-y$ 
Also, $x>y$ $\Rightarrow \dfrac{1}{x}<\dfrac{1}{y}$
Hence, B is correct option.

Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

In expressing a length $81.472 \ km$ as nearly as possible with three significant digits, the percent error is

  1. $0.34\%$
  2. $0.034\%$
  3. $0.0034\%$
  4. $0.0038\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$81.472 km = 81472$ meters $= 81500$ meters with three significant digits.
$\displaystyle \therefore Error\%=\frac{81500-81472}{81472}\times 100=0.034\%$

Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

If $a, b, c$ are distinct $+ve$ real numbers and ${ a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }=1$ then $ab + bc + ca$ is 

  1. less then $1$
  2. equal to $1$
  3. greater then $1$

  4. any real no.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

${a}^{2} + {b}^{2} + {c}^{2} = 1 \quad \left( \text{Given} \right)$


${\left( a +  b + c \right)}^{2} > 0$

${a}^{2} + {b}^{2} + {c}^{2} + 2 \left( ab + bc + ca \right) > 0$

$1 + 2 \left( ab + bc + ca \right) > 0$

$2 \left( ab + bc + ca \right) > -1$

$\Rightarrow ab + bc + ca >-\dfrac 12$

Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

If the decimal o.d25d25d25 ................ is expressible in the form n/27, then d+n must be

  1. 9

  2. 28

  3. 30

  4. 34
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$x = 0.d25 d25d25 -----$
$x = 0.\overline{d25}$
$1000 x = d25. \overline{d25}$
$999 x = d 25$
$x = \displaystyle \frac{d 25}{999}$
$x = \displaystyle \frac{d25}{37.27}$
take d = 9 then $x = \displaystyle \frac{25}{27}$
$d = 9          n = 25$
$d + n = 34$

Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

A $3$ digit id a $3$ digit number (not starting with zero) which reads the same backwards as forwards. For example $171$. The sum of all even $3$ digit palindromes, is 

  1. $22380$
  2. $25700$
  3. $22000$
  4. $22400$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A 3-digit palindrome is of the form ABA. For it to be even, A must be 2, 4, 6, or 8. B can be 0-9. For each A, there are 10 possibilities for B. Summing these values: 202+212+...+292, 404+414+...+494, etc. The sum is 22380.

Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

Which of the following statements is incorrect regarding significant figures?

  1. All the non-zero digits are significant.

  2. All the zeros between two non-zero digits are significant.

  3. Greater the number of significant figures in a measurement, smaller is the percentage error.

  4. The power of 10 is counted while counting the number of significant figures.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The term significant figures are referring to the number of important digits (0 through 9 inclusive) in the coefficient of some expression in the scientific notation. The number of significant figures in any expression indicate the confidence or precision with which we can state a quantity.

Some rules for significant figures are:

1. All non-zero numbers are significant.

2. Zeros located between non-zero digits are significant.

3. Trailing zeros at the end will be significant only if the number contains a decimal point; otherwise, they are insignificant.

4. Zeros to the left of the first nonzero digit are insignificant.

5. Number in exponents (for example power of 10) is insignificant.

Thus option D is correct.